Question

Suppose you just bought a 20-year annuity of $7,800 per year at the current interest rate of 10 percent per year.

What is the value of your annuity today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Present value

$

What happens to the value of your investment if interest rates suddenly drop to 5 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Present value

$

What if interest rates suddenly rise to 15 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Present value

$

Answer 1

Answer a.

Annual Payment = $7,800
Period of Annuity = 20 years
Annual Interest Rate = 10%

Present Value of Annuity = $7,800 * PVIFA(10%, 20)
Present Value of Annuity = $7,800 * (1 - (1/1.10)^20) / 0.10
Present Value of Annuity = $7,800 * 8.51356
Present Value of Annuity = $66,405.77

Answer b.

Annual Payment = $7,800
Period of Annuity = 20 years
Annual Interest Rate = 5%

Present Value of Annuity = $7,800 * PVIFA(5%, 20)
Present Value of Annuity = $7,800 * (1 - (1/1.05)^20) / 0.05
Present Value of Annuity = $7,800 * 12.46221
Present Value of Annuity = $97,205.24

Answer c.

Annual Payment = $7,800
Period of Annuity = 20 years
Annual Interest Rate = 15%

Present Value of Annuity = $7,800 * PVIFA(15%, 20)
Present Value of Annuity = $7,800 * (1 - (1/1.15)^20) / 0.15
Present Value of Annuity = $7,800 * 6.25933
Present Value of Annuity = $48,822.77